In the manufacture of plywood, it is customary to utilize substantially rectangular scraps or small pieces or sheets of inexpensive and/or inferior veneer to form the layers or laminae of the core and to fasten together the small sheets edge-to-edge by continuous strings or threads which are secured to said sheets by adhesive or stitching and thereby provide a composite strip. A number of strips are assembled to form a full size core layer and additional layers are added until the core is of the desired thickness. It is readily apparent that stitching or sewing and adequate gluing require the use of relatively complicated equipment which increases the cost of manufacture, since stitching necessitates passing of strings through the sheets and/or around portions thereof and the mere gluing of strings to one of the faces of said sheets has proven to be insufficient to permit the necessary handling of the composite strips without disintegration thereof.